Question

On a standardized exam, the scores are normally distributed with a mean of 170 anda standard deviation of 40. Find the Z-score of a person who scored 70 on the exam.Answer:Submit Answer

Answer 1

To calculate the Z-score for a score of 70 on an exam with a mean of 170 and standard deviation of 40, subtract the mean from the score and then divide by the standard deviation. The calculated Z-score is -2.5, indicating the score is 2.5 standard deviations below the mean.

Step-by-step explanation:

The question asks to find the Z-score for a person who scored 70 on an exam, given that the scores on the exam are normally distributed with a mean (μ) of 170 and a standard deviation (σ) of 40. The formula for calculating a Z-score is z = (X - μ) / σ, where X is the score of interest.

To calculate the Z-score for a person who scored 70:

1. Subtract the mean from the score: 70 - 170 = -100.
2. Divide this result by the standard deviation: -100 / 40 = -2.5.
3. The Z-score is therefore -2.5.

This means the score of 70 is 2.5 standard deviations below the mean.

Answer 2

In a normal distribution, the formula for calculating z score is expressed as

z = (x - μ)/σ

where

σ is the population standard deviation

x is the sample mean

μ is the population mean

From the information given,

x = 70

μ = 170

σ = 40

By substituting these values into the formula,

z = (70 - 170)/40

z = - 2.5

The z score is - 2.5